Question: Solve for $x$ : $7\sqrt{x} + 5 = 4\sqrt{x} + 7$
Explanation: Subtract $4\sqrt{x}$ from both sides: $(7\sqrt{x} + 5) - 4\sqrt{x} = (4\sqrt{x} + 7) - 4\sqrt{x}$ $3\sqrt{x} + 5 = 7$ Subtract $5$ from both sides: $(3\sqrt{x} + 5) - 5 = 7 - 5$ $3\sqrt{x} = 2$ Divide both sides by $3$ $\frac{3\sqrt{x}}{3} = \frac{2}{3}$ Simplify. $\sqrt{x} = \dfrac{2}{3}$ Square both sides. $\sqrt{x} \cdot \sqrt{x} = \dfrac{2}{3} \cdot \dfrac{2}{3}$ $x = \dfrac{4}{9}$